Question

Find the volume of a cone with a base diameter of 9 and a height of 12. Write the exact volume in terms of pi , and be sure to include the correct unit in your answer.

Answer 1

81π cubic units

Explanation:

The formula for volume of cone is given by:

V = 1/3πr^2h, where

• V is the volume in cubic units,
• r is the radius of the circular base,
• and h is the height of the cone.

Step 1: Find radius:

We know that the diameter, d, is simply twice the radius. Thus, we can find the radius of the circular base by dividing the given diameter by 2:

d = 2r

d/2 = r

9/2 = r

4.5 units = r

Thus, the radius of the circular base is 4.5 units.

Step 2: Find volume and leave in terms of pi:

We can find the volume in terms of pi by plugging in 4.5 for r and 12 for h and simplifying:

V = 1/3π(4.5)^2(12)

V = 1/3π(20.25)(12)

V = 1/3π(243)

V = 81π cubic units

Thus, the volume of the cone in terms of pi is 81π cubic units.

Answer 2

Volume of a cone is 1/3Bh so your base 20.25(pi) and height is 12, times that and itll make 243, divided by the 1/3 is 81

81 is your volume